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This paper presents neural networks iterative learning control for a class of nonlinear time-varying systems. A finite time boundary layer is introduced and the inherent property of terminal sliding modes is exploited to realize finite time convergence, in the presence of initial repositioning errors. The neural networks employed in the controls have time-varying weights. Both indirect and direct neural learning controllers are designed, respectively, where efficient learning algorithms are proposed for training the time-varying neural networks. It is shown that the complete tracking is achieved over a pre-specified time interval, and all the signals in the closed-loop system remain bounded.